Amplify and forward relay method

ABSTRACT

The amplify and forward relay method enhances QOS in wireless networks and is based on the switch-and-examine (SEC) and SEC post-selection (SECps) diversity combining techniques where only a single relay out of multiple relays is used to forward the source signal to the destination. The selection process is performed based on a predetermined switching threshold. Maximal-ratio combining (MRC) is used at the destination to combine the signal on the relay path with that on the direct link.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a data communication network supportingmobile devices, and particularly to an amplify and forward relay methodthat provides reliable data transmission in such a data communicationnetwork using relay stations.

2. Description of the Related Art

In wireless applications, users may not be able to support multipleantennas due to size, complexity, and power limitations. Cooperativediversity is a promising solution for such a condition. Among the knownrelaying schemes are the amplify-and-forward (AF) and thedecode-and-forward (DF). In the AF scheme, the relay simply amplifiesthe source signal before forwarding it to the destination. In the DFscheme, some signal processing needs to be performed before the signalis forwarded. In systems where multiple relays are used, efficientrelaying protocols, e.g., fixed, selection, and incremental relaying,have been proposed. In fixed relaying, a set of relays is used toforward the source signal to the destination. In selection relaying, arelay or a number of relays is selected to cooperate according theconditions of their channels. Finally, in incremental relaying, a relayor a set of relays is asked to cooperate based on a feedback signal fromthe destination if the direct link channel is under a certain threshold.

Other technologies include user cooperation in a coded cooperativesystem, where convolutional codes are used in a Rayleigh fadingenvironment with path loss effect. Opportunistic relaying is a scheme inwhich the relay with the strongest end-to-end (e2e) signal-to-noiseratio (SNR) is selected to cooperate with the source. Hence, thechannels of all relays need to be estimated each time in order to selectthe best relay among all relays. A study on centralized selectionrelaying has been presented in which all channel gains are assumed to beavailable at the destination node in order to select the best relayamong all relays. Additionally, a known partial relay selection schemefor AF (amplify-and-forward) relay networks provides a relay selectionalgorithm where the relay with the SNR that is greater than apredetermined SNR threshold and is the maximum among other relays ischosen to be the best. In another selection relaying method, theprotocol selects the second or even the N^(th) best relay with thehighest end-to-end (e2e) SNR in the case when the first best relay isinvolved in some scheduling or load balancing schemes. Other schemesinclude the one where the relay with the best minimum of the two hopchannels is selected as the best, and another one where the relay withthe best value of a modified expression of the harmonic mean is selectedto cooperate with the source.

In relay selection schemes for channel state information (CSI)-assisteddual-hop AF relay networks over Nakagami-m fading channels, the key ideais that the selection criterion is based on the channel magnitudes andnot the channel SNRs, which is an attempt to reduce the systemcomplexity. In incremental opportunistic relaying, the best relay isasked to cooperate if the direct link channel is below a predeterminedSNR threshold. Additionally, energy-fair decentralized relay selectiontechniques in wireless sensor networks whose nodes are uniformlydistributed according to a two-dimensional homogeneous Poisson processhave been developed. These schemes take the network topologicalstructure into consideration. Other researchers have proposed a relayselection scheme for half-duplex relays with buffers. This protocolguarantees that each time, the best first hop and second hops links areinvolved in the data transmission.

As can be seen, most of the aforementioned methods suffer from a heavyestimation load. As an example, in the best relay selection scheme, allchannels of all relays need to be estimated each transmission time. Onthe other hand, in the partial relaying protocol, half this estimationload is required each time. This means more power consumption, lowbattery life, and high system complexity. In most wireless networks,once the minimum system requirement is achieved, no more operations thatincrease the system complexity need to be done. This finds itspracticality in both sensor and ad-hoc networks.

Thus, an amplify and forward relay method solving the aforementionedproblems is desired.

SUMMARY OF THE INVENTION

The amplify and forward relay method enhances quality of service (QOS)in wireless networks and is based on the switch-and-examine (SEC) andSEC post-selection (SECps) diversity combining technique where only aselected relay out of multiple relays is used to forward the sourcesignal to the destination. The selection process is performed based on apredetermined switching threshold. Maximal-ratio combining (MRC) is usedat the destination to combine the signal on the relay path with that onthe direct link.

These and other features of the present invention will become readilyapparent upon further review of the following specification anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an embodiment of an amplify and forwardrelay method according to the present invention, illustrating a dual hopAF relay system.

FIG. 2 is a flowchart of an embodiment of an amplify and forward relaymethod according to the present invention, illustrating the SEC relayingmethod.

FIG. 3 is a flowchart of an embodiment of an amplify and forward relaymethod according to the present invention, illustrating the SECpsrelaying method.

Similar reference characters denote corresponding features consistentlythroughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

At the outset, it should be understood by one of ordinary skill in theart that embodiments of the present method can comprise software orfirmware code executing on a computer, a microcontroller, amicroprocessor, or a DSP processor; state machines implemented inapplication specific or programmable logic; or numerous other formswithout departing from the spirit and scope of the method describedherein. The present method can be provided as a computer program, whichincludes a non-transitory machine-readable medium having stored thereoninstructions that can be used to program a computer (or other electronicdevices) to perform a process according to the method. Themachine-readable medium can include, but is not limited to, floppydiskettes, optical disks, CD-ROMs, and magneto-optical disks, ROMs,RAMs, EPROMs, EEPROMs, magnetic or optical cards, flash memory, or othertype of media or machine-readable medium suitable for storing electronicinstructions.

The amplify and forward relay method enhances QOS in wireless networksand is based on the switch-and-examine (SEC) and SEC post-selection(SECps) diversity combining technique where only a selected relay out ofmultiple relays is used to forward the source signal to the destination.The selection process is performed based on a predetermined switchingthreshold. Maximal-ratio combining (MRC) is used at the destination tocombine the signal on the relay path with that on the direct link. Themethod can be implemented in both the downlink and uplink channels. Thepresent method selects the switching threshold to minimize the errorprobability of the system. The direct link between the source and thedestination has an important role in wireless systems and is utilized inthe present method. The threshold in the present method is asignal-to-noise ratio (SNR) and is most appropriately related to circuitswitching mode relay networks. Thus, the present method is achannel-state-information (CSI)-assisted AF relay selection scheme.Moreover, in the present relay selection scheme, the relay's two hopchannels are considered in the selection process, and not just thechannels of one hop.

Only one relay is selected to forward the source signal to thedestination according to a certain predetermined switching threshold.The switching threshold is evaluated to minimize the error rate, andthus fulfills certain performance requirements. In contrast to theaforementioned relay selection schemes, the proposed scheme reduces thenumber of channel estimations, and thus the system complexity. In thepresent protocol, the channels of only an arbitrary relay are requiredto be estimated each time of data transmission. In this case, the otherrelays remain silent and do not need to operate as channel estimators.This saves the power of these nodes, as well as their battery life. Amoment-generating function (MGF) of the SNR at the output of theselection scheme is derived. Then, we evaluate the CDF, and hence theoutage probability of the end-to-end (e2e) SNR at the output of the MRCcombiner. Finally, we evaluate an expression for the BER (bit errorrate) of the whole system. An upper bound on the e2e SNR is used in theanalysis, and both independent identical distributed (i.i.d.) andindependent non-identical distributed (i.n.d.) relay paths areconsidered.

In the SEC selection relaying system 10, shown in FIG. 1, a source node12 communicates with a destination node 14 through the direct link and arelay path. At the guard period of each transmission, a ready-to-send(RTS) packet and a clear-to-send (CTS) packet are sent from the sourceand the destination, respectively. From these signals, an arbitraryrelay out of M relays, 18 a, 18 b, 18 c estimates its instantaneouschannels. Then, the minimum magnitude of the two hops is compared with apredetermined switching threshold. If this minimum magnitude is largerthan the switching threshold, then this relay is selected to forward thesource signal, and a short duration flag packet is sent from this relayto the other relays, signaling its presence. Otherwise, a flag packet issent from this relay to another relay asking it to estimate itschannels, which is then to be compared with the switching threshold.This process continues until a relay satisfying the switching thresholdis found, or until reaching the last relay. In this case, the last relayis chosen to forward the source signal. As an enhancement on the SECrelaying, the present method utilizes an SECps relaying scheme, wherefor the case in which the last relay is reached and found unacceptable,the SECps scheme goes and selects the best relay among all relays.

Usually, in practical applications, the predetermined switchingthreshold is chosen in order to satisfy certain performance requirementsin terms of the outage probability or error probability. In our proposedscheme, the SNRs of both the first hop and the second hop channels ofthe selected relay are required at the destination node. These SNRvalues, along with the direct link SNR, are then used in calculating theswitching threshold in such a way that the end-to-end (e2e) bit errorprobability (BEP) is minimized. The flowcharts of the present SEC andSECps relaying schemes are shown in FIGS. 2 and 3, respectively As shownin FIG. 2, the present SEC method 200 includes a starting step 202 thatinitializes i and Γ. Another of the relays, shown in FIG. 1, is includedat step 204. Then, at step 206, y_(S,R) _(i) and y_(R) _(i) _(,D) areestimated. At step 208, a check is performed to determine ifγ_(i)=min(γ_(S,R) _(i) ,γ_(R) _(i) _(,D)>γ_(T)) or i=M, and if thoseconditions are not met, then the process iterates through steps 204,206, and 208. Otherwise, Γ is set to γ_(i) at step 210, and the SECprocedure is terminated. The SEC post-selection (SECps) method 300,shown in FIG. 3 starts by initializing i and Γ at step 302. At step 304another of the relays, shown in FIG. 1, is included. At step 306,y_(S,R) _(i) and y_(R) _(i) _(,D) are estimated. At step 308 a check isperformed to determine if γ_(i)=min(γ_(S,R) _(i) ,γ_(R) _(i)_(,D)>γ_(T)). If true, then Γ is set to γ_(i) at step 310, and the SECprocedure is terminated at step 316. If not true, then at step 312, acheck is performed to determine whether i=M. If i=M, then at step 314, Γis set to max{γ_(i)}_(i=1) ^(M) and the SECps procedure terminates atstep 316. On the other hand, if at step 312 i≠M, then the procedureiterates beginning at step 304 until the stopping criterion is reachedat step 316.

At the destination, MRC (maximal ratio combining) is used to combine thesignal on the direct path and that through the relay. The channelcoefficients between the source and the i^(th) relay Ri(h_(S,Ri)),between Ri and D (h_(Ri,D)) and between S and D (h_(S,D)) are assumed tobe flat Rayleigh fading gains. In addition, h_(S,Ri), h_(Ri,D), andh_(S,D) are mutually-independent and non-identical. We also assume here,without any loss of generality, that the additive white Gaussian noise(AWGN) terms of all links have zero means and equal variance N₀/2.

Communications occur in two phases. In phase 1, the source transmits themodulated signal x with unit energy to the destination and the tworelays. The received signals at the destination and the i^(th) relay,respectively, satisfy the equations:

y _(S,D) =h _(S,D)√{square root over (E _(S) s)}+n _(S,D)  (1)

y _(S,R) _(i) =h _(S,R) _(i) √{square root over (E _(S) s)}+n _(S,R)_(i)   (2)

where Es is the average symbol energy, and n_(S,D) and n_(S,R) _(i) arethe AWGN between S and D and S and R_(i), respectively. The relay chosenby the SEC method 200 amplifies the received signal and transmits it tothe destination in the second phase of communication. During this phase,the received signal at the destination from the selected relay is:

y _(R) _(sel) _(,D) =Gh _(R) _(sel) _(,D)√{square root over (E _(S)s)}+n _(R) _(sel) _(,D)  (3)

where G is the active relay amplifying gain, chosen asG²=E_(S)/(E_(S)h_(S,R) _(sel) ²+N₀). It is widely known that thecomposite SNR of the relay link can be written as:

$\begin{matrix}{\gamma_{S,R_{i},D} = \frac{\gamma_{S,R_{i}}\gamma_{R_{i},D}}{\gamma_{S,R_{i}} + \gamma_{R_{i},D} + 1}} & (4)\end{matrix}$

where γ_(S,R) _(i) =h_(S,R) _(i) ²E_(S)/N₀ is the instantaneous SNR ofthe source signal at Ri and γ_(R) _(i) _(,D)=h_(R) _(i) _(,D) ²E_(S)/N₀is the instantaneous SNR of the relay signal (by Ri) at D. By usingMaximal-ratio combining (MRC) at the destination node, the total SNR atthe combiner output is simply the addition of the two random variablesat its inputs as follows:

γ_(tot)=γ_(S,D)+γ_(SEC)  (5)

where γ_(S,D)=h_(S,D) ²E_(S)/N₀ is the instantaneous SNR between S andD, and γ_(SEC) is the SNR at the output of the SEC selection scheme. Tosimplify the ensuing derivations, equation (4) should be expressed in amore mathematically tractable form. A tighter upper bound for γ_(S,R)_(i) _(,D) is given in by:

γ_(S,R) _(i) _(,D)≦γ_(i)=min(γ_(S,R) _(i) _(,D),γ_(R) _(i) _(,D))  (6)

Assuming Rayleigh fading channels between source, relays, anddestination, the distribution of γ_(i) in equation (6) is exponential,and hence its PDF can be expressed in terms of the average SNR γ _(S,R)_(i) =E[h_(S,R) _(i) ²]E_(S)/N₀ and γ _(R) _(i) _(,D)=E[h_(R) _(i) _(,D)²]E_(S)/N₀ (where E[.] is the expectation operator) as:

$\begin{matrix}{{f_{{\gamma \;}_{i}}(\gamma)} = {\frac{1}{\gamma_{i}}{\exp \left( {- \frac{\gamma}{\gamma_{i}}} \right)}}} & (7)\end{matrix}$

where γ _(i)= γ _(S,R) _(i) γ _(R) _(i) _(,D)/( γ _(S,R) _(i) + γ _(R)_(i) _(,D)). Subsequent analysis is based on the SNR bound given inequation (6) on the e2e SNR of the selection scheme.

With respect to the outage probability, for independent identicaldistributed (i.i.d.) relay paths, the cumulative distribution function(CDF) of γ_(SEC) can be written as:

$\begin{matrix}{{F_{\gamma \; {SEC}}(\gamma)} = \left\{ \begin{matrix}{{\left\lbrack {F_{\gamma}\left( \gamma_{T} \right)} \right\rbrack^{M - 1}{F_{\gamma}(\gamma)}},} & {{\gamma < \gamma_{T}};} \\{{{\sum\limits_{j = 0}^{M - 1}{\left\lbrack {{F_{\gamma}(\gamma)} - {F_{\gamma}\left( \gamma_{T} \right)}} \right\rbrack \left\lbrack {F_{\gamma}\left( \gamma_{T} \right)} \right\rbrack}^{j}} + \left\lbrack {F_{\gamma}\left( \gamma_{T} \right)} \right\rbrack^{M}},} & {\gamma \geq \gamma_{T}}\end{matrix} \right.} & (8)\end{matrix}$

where M is the number of relays and γ_(T) is the predetermined switchingthreshold. The CDF of the i^(th) relay path can be found as:

$\begin{matrix}{{F_{\gamma_{i}}(\gamma)} = {1 - {\exp \left( {- \frac{\gamma}{\gamma_{i}}} \right)}}} & (9)\end{matrix}$

where γ_(i) is as defined before. Differentiating (9) with respect to γ,and after some simple manipulations, the moment-generating function(MGF) of γ_(SEC) can be found as:

$\begin{matrix}{{M_{\gamma_{SEC}}(s)} = {\left( {1 - {\overset{\_}{\gamma}\; s}} \right)^{- 1}{\quad\left\lbrack {\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{M - 1} + {{\exp \left( {- \left( {\frac{\gamma_{T}}{\gamma} - {\gamma \; T^{S}}} \right)} \right)} \times {\sum\limits_{j = 0}^{M - 2}\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{j}}}} \right\rbrack}}} & (10)\end{matrix}$

where we have assumed i.i.d. symmetrical hops, i.e., γ _(S,R) _(i) = γ_(R) _(i) _(,D)= γ·∀i, iε{1, . . . , M} in the last result. UsingMaximal-ratio combining (MRC) at the destination, the MGF of the totalSNR is given by:

M _(γ) _(tot) (s)=M _(γ) _(S,D) (s)M _(γ) _(SEC) (s).  (11)

Using partial fractions, the last result of the MGF of the total SNR canbe found as:

$\begin{matrix}{{M_{\gamma_{tot}}(s)} = {{\left( {1 - {\exp \left( {- \frac{2\; \gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{M - 1}\left\lbrack {\frac{\left( {{1 - {\overset{\_}{\gamma}\; S}},D^{s}} \right)^{- 1}}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} + \frac{\left( {1 - {\overset{\_}{\gamma}}_{S}} \right)^{- 1}}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}} \right)}} \right\rbrack} + {{\exp\left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)} \times {\sum\limits_{j = 0}^{M - 2}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{j}{\quad{\left\lbrack {\frac{\left( {{1 - {\overset{\_}{\gamma}\; S}},D^{s}} \right)^{- 1}{\exp \left( {\gamma \; T^{S}} \right)}}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} + \frac{\left( {1 - {\overset{\_}{\gamma}}_{S}} \right)^{- 1}{\exp \left( {\gamma \; T^{S}} \right)}}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}} \right)}} \right\rbrack.}}}}}}} & (12)\end{matrix}$

Taking the inverse Laplace transform of equation (12), after some simplesteps, yields:

$\begin{matrix}{P_{out} = {\frac{1}{\left( {\overset{\_}{\gamma} - {\overset{\_}{\gamma}}_{S,D}} \right)}\left\{ {\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{M - 1}{\left. \quad{\left\lbrack {{\overset{\_}{\gamma}\left( {1 - {\exp \left( {- \frac{\gamma_{th}}{\overset{\_}{\gamma}}} \right)}} \right)} - {{\overset{\_}{\gamma}}_{S,D}\left( {1 - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right)}} \right\rbrack \times {\sum\limits_{j = 0}^{M - 2}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{j}\left\lbrack {{\overset{\_}{\gamma}\left\{ {{\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)} - {\exp \left( {- \frac{\gamma_{th}}{\overset{\_}{\gamma}}} \right)}} \right\}} - {{\overset{\_}{\gamma}}_{S,D}{\exp \left( {\left( {{- \frac{1}{\overset{\_}{\gamma}}} + \frac{1}{{\overset{\_}{\gamma}}_{S,D}}} \right)\gamma_{T}} \right)} \times \left\{ {{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right\}}} \right\rbrack}}} \right\}.}} \right.}} & (13)\end{matrix}$

For the i.n.d. case, the CDF of γ_(SEC) can be written as:

$\begin{matrix}{{F_{{\gamma \;}_{SEC}}(\gamma)} = \left\{ \begin{matrix}{{\overset{M - 1}{\sum\limits_{i = 0}}{\pi_{i}{F_{\gamma_{i}}(\gamma)}{\prod\limits_{\underset{k \neq i}{k = 0}}^{M - 1}\; {F_{\gamma_{k}}\left( {\gamma \; T} \right)}}}},{\gamma < \gamma_{T}}} \\{{\sum\limits_{i = 0}^{M - 1}\begin{pmatrix}{{\pi_{i}{\prod\limits_{k = 1}^{M}{F_{\gamma_{k}}\left( {\gamma \; T} \right)}}} +} \\{\sum\limits_{i = 0}^{M - 1}{{\pi_{{({({i - j})})}M}\left\lbrack {{F_{\gamma_{i}}(\gamma)} - {F_{\gamma_{i}}\left( {\gamma \; T} \right)}} \right\rbrack} \times}} \\{\prod\limits_{k = 0}^{j - 1}{F_{{\gamma {({({i - j + k})})}}_{M}}\left( {\gamma \; T} \right)}}\end{pmatrix}},{\gamma \geq \gamma_{T}},}\end{matrix} \right.} & (14)\end{matrix}$

where π_(i), 0, . . . , M−1 are the stationary distribution of anM-state Markov chain, and it is the probability that the i^(th) relay ischosen, F_(γ) _(i) (γ) is the CDF of signal power of the i^(th) relaypath, and ((i−j))_(M) denotes i−j modulo M. Following the same procedureas in the i.i.d. fading channels yields:

$\begin{matrix}{P_{out} = {\sum\limits_{i = 0}^{M - 1}{\pi_{i}{\prod\limits_{\underset{k \neq i}{k = 0}}^{M - 1}\; {\left( {1 - {\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{k}} \right)}} \right){\quad{\begin{bmatrix}{\frac{\left( {1 - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{i}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} + \frac{\left( {1 - {\exp \left( {- \frac{\gamma_{th}}{\overset{\_}{\gamma}}} \right)}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{{\overset{\_}{\gamma}}_{i}}} \right)} - {\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)}} \\\begin{Bmatrix}{\frac{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{i}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \times} \\\left( {{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right)\end{Bmatrix}\end{bmatrix} + {\sum\limits_{j = 0}^{M - 1}{\pi_{{({({i - j})})}_{M}} \times {\prod\limits_{k = 0}^{j - 1}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{{({({i - j + k})})}_{M}}}} \right)}} \right){\quad\left\lbrack {{\exp\left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{i}}} \right)} \begin{Bmatrix}{{\frac{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{i}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}\left( {1 - {\exp \left( {- \frac{\gamma_{th}}{\overset{\_}{{\overset{\_}{\gamma}}_{S,D}}}} \right)}} \right)} +} \\{\frac{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{{\overset{\_}{\gamma}}_{i}}} \right)} \times \left( {1 - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{i}}} \right)}} \right)}\end{Bmatrix}} \right\rbrack}}}}}}}}}}}} & (15)\end{matrix}$

With respect to bit error probability (BEP), the average BEP for Binaryphase-shift keying (BPSK) signals in terms of the moment-generatingfunction is given by:

$\begin{matrix}{{P_{b}(E)} = {\frac{1}{\pi}{\int_{0}^{\pi/2}{{M_{\gamma_{tot}}\left( {- \frac{1}{\sin^{2}\varphi}}\  \right)}{{\varphi}.}}}}} & (16)\end{matrix}$

Substituting (15) in (16) yields:

$\begin{matrix}{{P_{b}(E)} = {{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{M - 1}\left\lbrack {{\frac{1}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}I_{1}} + {\frac{1}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}} \right)} \times I_{2}}} \right\rbrack} + {{\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}{\sum\limits_{j = 0}^{M - 2}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{j} \times \left\lbrack {{\frac{1}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \times I_{3}} + {\frac{1}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}} \right)}I_{4}}} \right\rbrack}}}}} & (17)\end{matrix}$

where:

$I_{1} = {\frac{1}{\pi}{\int_{0}^{~{\pi/2}}{\frac{\sin^{2}\varphi}{{\sin^{2}\varphi} + {\overset{\_}{\gamma}}_{S,D}}{\varphi}}}}$$I_{2} = {\frac{1}{\pi}{\int_{0}^{\pi/2}{\frac{\sin^{2}\varphi}{{\sin^{2}\varphi} + \overset{\_}{\gamma}}{\varphi}}}}$$I_{3} = {\frac{1}{\pi}{\int_{0}^{\pi/2}{\frac{\sin^{2}\varphi \; {\exp \left( {- \frac{\gamma_{T}}{\sin^{2}\varphi}} \right)}}{{\sin^{2}\varphi} + {\overset{\_}{\gamma}}_{S,D}}{\varphi}}}}$$I_{4} = {\frac{1}{\pi}{\int_{0}^{\pi/2}{\frac{\sin^{2}\varphi \; {\exp \left( {- \frac{\gamma_{T}}{\sin^{2}\varphi}} \right)}}{{\sin^{2}\varphi} + \overset{\_}{\gamma}}{{\varphi}.}}}}$

The integrals I₁ and I₂ can be solved, and the integrations I₃ and I₄can be solved. After some algebraic manipulations, the last result ofthe bit error rate appears as:

$\begin{matrix}{{P_{b\;}(E)} = {\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{M - 1}{\quad{\left\lbrack {{\frac{1}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}\left( {1 - \sqrt{\frac{{\overset{\_}{\gamma}}_{S,D}}{1 + {\overset{\_}{\gamma}}_{S,D}}}} \right)} + {\frac{1}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}} \right)}\left( {1 - \sqrt{\frac{\overset{\_}{\gamma}}{1 + \overset{\_}{\gamma}}}} \right)}} \right\rbrack + {{\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}{\sum\limits_{j = 0}^{M - 2}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{j}\left\{ {{{\frac{1}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}\left\lbrack {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - {\frac{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{S,D}}}} \times {Q\left( \sqrt{{2\; \gamma_{T}} + \frac{2\; \gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}}} \right\rbrack} + {\frac{1}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\gamma}} \right)}\left. \quad\left\lbrack {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - {\frac{\exp \left( \frac{\gamma_{T}}{\overset{\_}{\gamma}} \right)}{\sqrt{1 + \frac{1}{\overset{\_}{\gamma}}}}{Q\left( \sqrt{{2\; \gamma_{T}} + \frac{2\; \gamma_{T}}{\overset{\_}{\gamma}}} \right)}}} \right\rbrack \right\}}},} \right.}}}}}}} & (18)\end{matrix}$

where Q(.) is the Gaussian Q-function. For the i.n.d. relay paths, andupon substituting the MGF of γ_(tot) for this case in equation (16), andfollowing the same procedure as in the i.i.d. case, a closed-formexpression for the BEP can be evaluated as:

$\begin{matrix}{{P_{b}(E)} = {\sum\limits_{i = 0}^{M - 1}{\pi_{i}{\prod\limits_{\underset{k \neq i}{k = 0}}^{M - 1}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{k}}} \right)}} \right){\quad{\left\lbrack {\frac{\left( {1 - \sqrt{\frac{{\overset{\_}{\gamma}}_{S,D}}{1 + {\overset{\_}{\gamma}}_{S,D}}}} \right)}{2\left( {1 - \frac{{\overset{\_}{\gamma}}_{i}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} + \frac{\left( {1 - \sqrt{\frac{{\overset{\_}{\gamma}}_{i}}{1 + {\overset{\_}{\gamma}}_{i}}}} \right)}{2\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{{\overset{\_}{\gamma}}_{i}}} \right)} - {\frac{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}\left\{ {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \right)}}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{S,D}}}}} \right\}} - {\frac{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{{\overset{\_}{\gamma}}_{i}}} \right)}\left\{ {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)} \right)}}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{i}}}}} \right\}}} \right\rbrack + {\sum\limits_{i = 0}^{M - 1}{\sum\limits_{j = 0}^{M - 1}{\pi_{{({({i - j})})}_{M}}{\prod\limits_{k = 0}^{j - 1}{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{{({({i - j + k})})}_{M}}}} \right)}} \right){\quad{\left\lbrack {{\frac{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{i}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}\left\{ {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - {\frac{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{S,D}}}} \times {Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \right)}}} \right\}} + {\frac{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{{\overset{\_}{\gamma}}_{i}}} \right)}\left\{ {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{i}}} \right)} \right)}}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{i}}}}} \right\}}} \right\rbrack.}}}}}}}}}}}}}} & (19)\end{matrix}$

Regarding SECps selection relaying, for the i.i.d. case, the CDF ofγ_(SECps) can be written as:

$\begin{matrix}{{F_{\gamma_{SECps}}(\gamma)} = \left\{ \begin{matrix}{{1 - {\sum\limits_{j = 0}^{M - 1}{\left\lbrack {F_{\gamma}\left( \gamma_{T} \right)} \right\rbrack^{j}\left\lbrack {1 - {F_{\gamma}(\gamma)}} \right\rbrack}}},} & {{\gamma < \gamma_{T}};} \\\left\lbrack {F_{\gamma}(\gamma)} \right\rbrack^{M,} & {\gamma \geq \gamma_{T}}\end{matrix} \right.} & (20)\end{matrix}$

Following the same procedure as in the i.i.d. case of the SEC relayingscheme results in:

$\begin{matrix}{P_{out} = {{\frac{\left( {1 - {\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{k}}} \right)}} \right)^{M}}{\left( {\overset{\_}{\gamma} - {\overset{\_}{\gamma}}_{S,D}} \right)}\left\lbrack {{\overset{\_}{\gamma}\; {\exp \left( \frac{\gamma_{T}}{\overset{\_}{\gamma}} \right)}\left( {{\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)} - {\exp \left( {- \frac{\gamma_{th}}{\overset{\_}{\gamma}}} \right)}} \right)} - {{\overset{\_}{\gamma}}_{S,D}{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)} \times \left( {{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right)}} \right\rbrack} + {\sum\limits_{j = 0}^{M - 1}\begin{matrix}{M - 1} \\j\end{matrix}\left( {- 1} \right)^{j}\frac{1}{\overset{\_}{\gamma} - {\left( {j + 1} \right){\overset{\_}{\gamma}}_{S,D}}}{\quad\left\lbrack {{\frac{\overset{\_}{\gamma}}{\left( {j + 1} \right)} \times \left( {1 - {\exp \left( {- \frac{\left( {j + 1} \right)\gamma_{th}}{\overset{\_}{\gamma}}} \right)}} \right)} - {{\overset{\_}{\gamma}}_{S,D}\left( {1 - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right)} - {{\exp \left( {- \frac{\left( {j + 1} \right)\gamma_{T}}{\overset{\_}{\gamma}}} \right)}\left\{ {{\frac{\overset{\_}{\gamma}\; {\exp \left( \frac{\left( {j + 1} \right)\gamma_{T}}{\overset{\_}{\gamma}} \right)}}{\left( {j + 1} \right)} \times \left( {{\exp \left( {- \frac{\left( {j + 1} \right)\gamma_{T}}{\overset{\_}{\gamma}}} \right)} - {\exp \left( {- \frac{\left( {j + 1} \right)\gamma_{th}}{\overset{\_}{\gamma}}} \right)}} \right)} - {{\overset{\_}{\gamma}}_{S,D}{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}\left( {{\exp \left( {- \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} - {\exp \left( {- \frac{\gamma_{th}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}} \right)}} \right\}}} \right\rbrack}}}} & (21)\end{matrix}$

Following the same procedure as in the i.i.d. case of the SEC selectionscheme, the BEP of the SECps relaying scheme can be evaluated as shownin equation (22).

Outage performance utilizing the present amplify and forward relaymethod for different values of outage threshold γ_(th) at the optimumswitching threshold γ_(T-Opt) revealed that as γ_(th) increases, thesystem performance becomes more degraded, as expected. SEC, and SEC+MRCschemes with optimal switching threshold γ_(T-Opt) add gain to systemperformance compared with a no diversity case.

The number of relays M and the switching threshold γ_(T) affectperformance in that increasing M leads to a significant gain in systemperformance, specially, in the medium SNR region. On the other hand, asγ_(T) becomes smaller or larger than the average SNR, the BEPimprovement decreases asymptotically to the case of two relays. This isdue to the fact that, if the average SNR is very small compared toγ_(T), all the relays will be unacceptable most of the time. On theother hand, if the average SNR is very high in compared to γ_(T), allthe relays will be acceptable and one relay will be used most of thetime. Thus, in both cases, the additional relays will not lead to anygain in system behavior.

$\begin{matrix}{{P_{b}(E)} = {{\left\lbrack {1 - \left( {1 - {\exp \left( {- \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)}} \right)^{M}} \right\rbrack \left\{ {{\frac{1}{\left( {1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)}\left( {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \right)}}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{S,D}}}}} \right)} + {\frac{1}{\left( {1 - \frac{{\overset{\_}{\gamma}}_{S,D}}{\gamma}} \right)}\left( {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\gamma_{T}}{\overset{\_}{\gamma}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{\overset{\_}{\gamma}}} \right)} \right)}}{\sqrt{1 + \frac{1}{\overset{\_}{\gamma}}}}} \right)}} \right\}} + {M{\sum\limits_{j = 0}^{M - 1}{\begin{matrix}{M - 1} \\j\end{matrix}\left( {- 1} \right)^{j} \times \left\lbrack {\frac{\left( {1 - \sqrt{\frac{{\overset{\_}{\gamma}}_{S,D}}{1 + {\overset{\_}{\gamma}}_{S,D}}}} \right)}{2\left( {j + 1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} + \frac{\left( {1 - \sqrt{\frac{\overset{\_}{\gamma}}{j + 1 + \overset{\_}{\gamma}}}} \right)}{2\left( {j + 1} \right)\left( {1 - {\left( {j + 1} \right)\frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}}} \right)} - {{\exp \left( \frac{{- \left( {j + 1} \right)}\gamma_{T}}{\overset{\_}{\gamma}} \right)}\left\{ {{\frac{1}{\left( {j + 1 - \frac{\overset{\_}{\gamma}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \times \left( {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\gamma_{T}}{{\overset{\_}{\gamma}}_{S,D}}} \right)} \right)}}{\sqrt{1 + \frac{1}{{\overset{\_}{\gamma}}_{S,D}}}}} \right)} + {\frac{1}{\left( {j + 1} \right)\left( {1 - {\left( {j + 1} \right)\frac{{\overset{\_}{\gamma}}_{S,D}}{\overset{\_}{\gamma}}}} \right)}\left( {{Q\left( \sqrt{2\; \gamma_{T}} \right)} - \frac{{\exp \left( \frac{\left( {j + 1} \right)\gamma_{T}}{\overset{\_}{\gamma}} \right)}{Q\left( \sqrt{2\left( {\gamma_{T} + \frac{\left( {j + 1} \right)\gamma_{T}}{\overset{\_}{\gamma}}} \right)} \right)}}{\sqrt{1 + \frac{\left( {j + 1} \right)}{\overset{\_}{\gamma}}}}} \right)}} \right\}}} \right\rbrack}}}}} & (22)\end{matrix}$

Simulations revealed that in a comparison between SEC, SECps, and bestrelay selection, SECps has nearly the same performance as the best relayselection for low SNR region. When the SNR increases, the errorperformance of the SECps scheme degrades and eventually becomes the sameas that of SEC. This is expected, since when γ_(T) is large incomparison with the average SNR, no relay will be acceptable and theSECps selection scheme will always select the best relay, just as inbest relay selection scheme; whereas, when γ_(T) is small compared tothe average SNR, the SECps selection scheme works more like conventionalSEC scheme. Moreover, comparison of the present method against popularexisting protocols revealed, in the exemplary case of 4 relays, thenumber of active relays in the best relay and partial relay selectionschemes is 4 all the time, whereas it is smaller in the case of thepresent scheme and depends on γ_(T). In the worst case, it reaches 3.For channel estimations, in the case of the best and partial relayselection schemes, 4 and 8 channels are required to be estimated,respectively, whereas, it is lower in the present protocols, whichreaches 6 at the worst case. This shows the significant reduction insystem complexity the present method achieves.

The effect of the relay positions on the average BEP performance fordifferent values of SNR was simulated. It is clear that in order to havebest performance for this AF relay system; the two relays must belocated midway between the source and the destination. In addition, asSNR increases, the system performance is more enhanced, as expected.

It is to be understood that the present invention is not limited to theembodiments described above, but encompasses any and all embodimentswithin the scope of the following claims.

We claim:
 1. In a cooperative wireless relay network of nodes, the nodesincluding a source, a set of relays, and a destination, an amplify andforward relay method performed during concurrent direct and relaycommunication between the source and the destination, the amplify andforward relay method comprising the steps of: arbitrarily selecting arelay from the set of relays; estimating a channel of the arbitrarilyselected relay; comparing a minimum magnitude of two hops of thearbitrarily selected relay path to a switching threshold; selecting thearbitrarily selected relay path as a route for the communication betweenthe source and the destination if the minimum magnitude exceeds theswitching threshold; and combining signals of the direct path and thearbitrarily selected relay path to enhance the concurrent direct andrelay communication.
 2. The amplify and forward relay method accordingto claim 1, further comprising the steps of: arbitrarily selecting asecond relay from said set of relays if said arbitrarily selected relayof claim 1 did not have a minimum magnitude exceeding said switchingthreshold, the arbitrarily selected second relay estimating its channelsto be compared with said switching threshold; continually arbitrarilyselecting from set of relays until a relay satisfying the switchingthreshold is found; and combining signals of said direct path and saidarbitrarily selected switching threshold satisfying relay's path toenhance said concurrent direct and relay communication.
 3. The amplifyand forward relay method according to claim 2, further comprising thesteps of: determining whether the last relay reached satisfies saidswitching threshold; selecting the best relay among all said relays insaid set of relays when the last relay reached does not satisfy saidswitching threshold; and combining signals of said direct path and saidbest relay's path to enhance said concurrent direct and relaycommunication.
 4. The amplify and forward relay method according toclaim 2, further comprising the step of deriving said switchingthreshold from an end-to-end (e2e) bit error probability (BEP)minimization, the BEP minimization being based on an averagesignal-to-noise ratio (SNR) of relay paths and direct link channels. 5.A computer software product, comprising a non-transitory medium readableby a processor, the non-transitory medium having stored thereon a set ofinstructions for performing an amplify and forward relay method for awireless communication system, the set of instructions including: (a) afirst sequence of instructions which, when executed by the processor,causes said processor to arbitrarily select a relay of from a set ofrelays in the communication system; (b) a second sequence ofinstructions which, when executed by the processor, causes saidprocessor to estimate a channel of said arbitrarily selected relaywherein channel state information (CSI) is collected; (c) a thirdsequence of instructions which, when executed by the processor, causessaid processor to minimize end-to-end (e2e) bit error probability (BEP)based on average signal-to-noise ratio (SNR) of relays and direct linkchannels; (d) a fourth sequence of instructions which, when executed bythe processor, causes said processor to determine a switching thresholdderived from the e2e BEP minimization; (e) a fifth sequence ofinstructions which, when executed by the processor, causes saidprocessor to compare a minimum magnitude of two hops of said arbitrarilyselected relay path to said switching threshold; (f) a sixth sequence ofinstructions which, when executed by the processor, causes saidprocessor to select said arbitrarily selected relay path as a route forsaid communication between said source and said destination if saidminimum magnitude exceeds said switching threshold; and (g) a seventhsequence of instructions which, when executed by the processor, causessaid processor to combine signals of said direct path and saidarbitrarily selected relay path to enhance said concurrent direct andrelay communication.
 6. The computer software product according to claim5, further comprising: an eighth sequence of instructions which, whenexecuted by the processor, causes said processor to arbitrarily select asecond relay of said set of relays if said arbitrarily selected relay ofclaim 1 did not have a minimum magnitude exceeding said switchingthreshold; a ninth sequence of instructions which, when executed by theprocessor, causes said processor to estimate said arbitrarily selectedsecond relay's channels to be compared with said switching threshold; atenth sequence of instructions which, when executed by the processor,causes said processor to continually arbitrarily select from said set ofrelays until a relay satisfying the switching threshold is found; and aneleventh sequence of instructions which, when executed by the processor,causes said processor to combine signals of said direct path and saidarbitrarily selected switching threshold satisfying relay's path toenhance said concurrent direct and relay communication.
 7. The computersoftware product according to claim 6, further comprising: a twelfthsequence of instructions which, when executed by the processor, causessaid processor to determine whether the last relay reached satisfiessaid switching threshold; a thirteenth sequence of instructions which,when executed by the processor, causes said processor to select the bestrelay among all said relays in said set of relays if said last relayreached does not satisfy said switching threshold; and a fourteenthsequence of instructions which, when executed by the processor, causessaid processor to combine signals of said direct path and said bestrelay's path to enhance said concurrent direct and relay communication.8. In a cooperative wireless relay network of nodes, the nodes includinga source, a set of relays, and a destination, an amplify and forwardrelay system operable during concurrent direct and relay communicationbetween said source and said destination, said amplify and forward relaysystem comprising: means for arbitrarily selecting a relay of said setof relays; means for estimating a channel of said arbitrarily selectedrelay wherein channel state information (CSI) is collected; means forminimizing end-to-end (e2e) bit error probability (BEP) based on averagesignal-to-noise ratio (SNR) of relays and direct link channels; meansfor determining a switching threshold derived from the e2e BEPminimization; means for comparing a minimum magnitude of two hops ofsaid arbitrarily selected relay path to said switching threshold; meansfor selecting said arbitrarily selected relay path as a route for saidcommunication between said source and said destination if said minimummagnitude exceeds said switching threshold; and means for combiningsignals of said direct path and said arbitrarily selected relay path toenhance said concurrent direct and relay communication.
 9. The amplifyand forward relay system according to claim 8, further comprising: meansfor arbitrarily selecting a second relay of said set of relays if saidarbitrarily selected relay of claim 1 did not have a minimum magnitudeexceeding said switching threshold; means for estimating channels ofsaid arbitrarily selected second relay to be compared with saidswitching threshold; means for continually arbitrarily selecting fromsaid set of relays until a relay satisfying the switching threshold isfound; and means for combining signals of said direct path and saidarbitrarily selected switching threshold satisfying relay's path toenhance said concurrent direct and relay communication.
 10. The amplifyand forward relay system according to claim 9, further comprising: meansfor determining whether the last relay reached satisfies said switchingthreshold; means for selecting the best relay among all said relays insaid set of relays if said last relay reached does not satisfy saidswitching threshold; and means for combining signals of said direct pathand said best relay's path to enhance said concurrent direct and relaycommunication.